MATEC Web of Conferences 22 , 030 1 7 (2015)
DOI: 10.1051/ m atec conf/ 2015 2 2030 1 7
C Owned by the authors, published by EDP Sciences, 2015
Design and Realization of Fitness Simulation Horse Based on Control
Theory
Lei Geng* & Gang Wu
Department of Public Fundation, Langfang Health Vocational College, Langfang, Hebei, China
ABSTRACT: As people’s living standard improves, they are increasingly concerned with health, and researches on various kinds of sports apparatus are also growing, such as the fitness simulation horse. In this paper, we
first described the advantages of the fitness simulation horse to the human body; then designed a fitness simulation horse platform with a new orthogonal parallel mechanism; set up the control system of fitness simulation
horse in an open structure; established a control model of fitness simulation horse, a structure model for
branched-chain control and a controller model based on the kinematics; validated these models in simulation
experiments; and last made a prospect on future development.
Keywords:
Control theory; Fitness simulation horse; Kinematics model
1 INTRODUCTION
The bionics has been highly focused at home and
abroad in recent years, and related research institutions have been founded in many universities and
scientific research institutes. The US and Japan have
kept ahead in their researches on bionics over the
world, whereas China is relatively backward. The
bionics is generated from the inspiration brought by
the creatures in nature. Increasingly growing bionics
researches have been made in the engineering field,
and certain achievements have been obtained.
Wang Ou, when studying the horse, was inspired to
construct a bionic horse. He used the MCU and a controller to build a bionic horse robot, tested it through
simulation, and then proved the feasibility of its electromechanical control system. Zhang Shouquan applied the bionics into the mechanical design, and discussed the functions and structures and broke a new
ground of bionics researches in the engineering field.
Zhang Wei et al. analyzed the kinematics of a running
horse, defined its kinematic sketch based on bionics,
and then analyzed all contact points on the horse body
to successfully prove the feasibility and rationality of
the designed system for a running horse. Zhao Jingbo
analyzed the bionic robot horse, set up a 6DOF kinematics model, and finally validated the correctness
and rationality of this model through simulation. Ren
Yuyan, when studying the relationship between the
physical changes and physiological changes in the
human body during movement, analyzed the effects of
the bionic horse on the body functions during movement, improved the ability of the bionic horse to receive a variety of information at the learning stage by
changing the algorithm, and finally realized the real-time control on the fitness simulation horse during
the experiment.
This paper, based on the results of previous re-
searches, constructed a fitness simulation horse based
on the control theory, set up a control platform of
fitness simulation horse by analyzing the kinematics
principles of human body and horse and then validated
this control platform in the experiment, thus laying the
theoretical foundation for the implementing this control platform.
2 CONTROL DESIGN AND IMPLEMENTATION
OF FITNESS SIMULATION HORSE
As limited by various conditions, few people can ride
a horse in real life, but more people prefer to ride a
simulation robot horse to keep fit. Although the researches on this robot are now growing, but most of
them are still at the beginning stage. For this reason,
the fitness simulation horse was further studied in this
paper based on these previous researches.
2.1 Mechanism Design of Fitness Simulation Horse
A good structural performance is needed to obtain the
rationality and stability of actions made by the fitness
simulation horse. As a result, this paper set up an improved Steward Platform mechanism model to reduce
the mechanism complexity.
The improved Steward platform is a 3D-platform
parallel mechanism, mainly consisting of the base,
branched chains and platform, as shown in the figure
1.
Main characteristics of this platform layout include:
1) Three branched chains are respectively perpendicular to the motion platform, and the applied parallel
mechanism has higher bearing capacity and is characterized by good distortionless coupling.
2) The hinge points on the motion platform are also
the connecting points on the base, similar to the translational pair.
*Corresponding author: 35372989@qq.com
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Article available at http://www.matec-conferences.org or http://dx.doi.org/10.1051/matecconf/20152203017
MATEC Web of Conferences
gration and development of current techniques rather
than implemented by the designer itself by every piece.
Therefore, proper plates and controllers may be selected to be integrated and a control system is developed in the design of fitness simulation horse, so as to
achieve high precision, quick response and good stability. In view of this, the control theory of fitness
simulation horse needs to meet following requirements:
1) Quite able to control the points, and also improve
the expansion and openness capabilities and enhance
the flexibility and freedom as actually required;
2) 6 branched chains of the fitness simulation horse
are mutually coordinated, completely controlled by the
control system, and strongly sensitive and quickly
responsive to motion commands;
3) The human-machine interface is fitted properly.
As the connection between the fitness simulation
horse and the human body, it not only can simulate the
state of motion of fitness simulation horse to grasp its
current movement condition, but also can be operated
to control the system.
Figure 1. Fitness Horse Structure Simulation Platform
3) Every branched chain constitutes a branch composed of the translational pair, connecting rod and ball
joint. The hinge center on the motion platform is perpendicular to the platform, and the ball joint of every
branched chain is centered on the corresponding platform.
2.2 Control System of Fitness Simulation Horse
In order to achieve a stable system, quick response
and high precision control, the structure of fitness
simulation horse needs to be analyzed and studied. As
it is a multi-axis real-time motion control system, the
effectively way to assure the coordination among all
kinematic branched chains for associated movement is
to analyze the system functions and subsequently set
up reasonable and valid control platform.
2.2.1 Control Theory Principles of Fitness Simulation Horse
The fitness simulation horse is designed through inte-
Monitor
2.2.2 Control System Structure of Fitness Simulation
Horse
Based on the control theory above, the multi-axis motion controller and the NC-embedded PC structure are
applied to building up the motion control system,
which can reduce the cost and improve the integration
between open mode structure and information.
Three systems are constructed for the fitness simulation horse by the functional needs and structures –
drive system, control system and user system, among
which the structure of control system is shown in the
figure 2.
1) Drive system: Realize the motion of fitness simulation horse as ordered by the command from control
system; meanwhile, the detection information can be
fed back to the inside of drive system to control the
motor position and speed.
2) Motion control system: This system is mainly to
generate the trajectory of fitness simulation horse and
process the host commands, realizing the host movement with information feedback and thus processing a
variety of information.
User Layer
External
controller
Control system
layer
Drive
User system
Figure 2. Fitness Horse Simulation Control Structure of Hardware Platform
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3) User system: This system bridges the information
between a host and fitness simulation horse and then
exchanges the information to run the system. In addition, it can also calculate the motion position and state
of the fitness simulation horse to execute the user’s
control commands.
3 MOTION CONTROL MODEL OF FITNESS
SIMULATION HORSE
The kinematics theory is the important foundation for
constructing a fitness simulation horse, mainly concerning the relationship between the joint end trajectory and joint variables. With all joint parameters assumed to be known, the end posture of fitness simulation horse can be identified based on kinematics, and
when the end effector is determined and specially
postured, the parameters of every joint can also be
identified based on kinematics, so that the movement
of fitness simulation horse is precisely controlled. This
shows the establishment of kinematical equations for
the fitness simulation horse is of great significance to
the control theory study.
3.1 Rigid Body Transformation Model
Generally, the used 3D coordinate system of rigid
body is Cartesian coordinate system. Suppose the
position of any one point in the space is Q , the corresponding vector is AQ , the rectangular coordinate
system is {A} and positions of point AQ respectively corresponding to axes X, Y and Z are
QX , Q Y, QZ , and then the position vector AQ can be
represented as:
Q QX i Q Y j QZk
A
(1)
A
Q represented in the matrix form is as follows:
QX Q Q Y [QX Q Y QZ ]T
QZ A
R X B
A
A
YB
A
Z B A
B
R 1 BA RT
A
B
RT 1
The rotation transformation of any kinds is obtained
from the basic rotation transformation of axes
X, Y, Z , and the basic rotation transformation matrices of rotation angle are:
0
1
R( X , ) 0 cos 0 sin cos R(Y, ) 0
sin cos R(Z, ) sin 0
sin cos (4)
0 sin 1
0 0 cos (5)
0
sin 0
0 1 cos 0
(6)
In the above equations, the position vector is used
to identify the point position, and the rotation matrix is
also used to identify the orientation of rigid body. The
spatial position and posture of the object is determined
by linking the coordinate system and object together,
and the origin of the coordinates is generally selected
on the object characteristic point. Take {B} as the
example, and then the rigid body B is in {B} :
{B} BA R
When
(2)
QB 0 A
QB 0 0 , it refers to
A
(7)
the object direction;
A
when B R =I , it refers to the object position.
In order to identify the position of B in the space,
another coordinate system {B} needs to be established, and then the corresponding unit vectors are
X B , YB , Z B . Link these two coordinate systems, and
then the corresponding equation is:
A
B
A
Therefore, B R is an orthogonal matrix, and its
product of inverse matrix and transpose is 1, that is:
(3)
A
B
Where, R is a 3×3 rotation matrix including
three independent elements, with corresponding constraints given as follows:
A
X B A X B AYB AYB AZ B AZ B 1
A
X B AYB AYB AYB AZ B A X B 0
p
The vectors
of the
spatial point
coordinate
A
B
system are Q and Q . The corresponding transformation relationship between them is:
Q BA R BQ AQB 0
A
(8)
Although the equation above is a non-homogeneous
equation, it can be represented as a homogeneous one
given below:
AQ BA R
1 0
QB 0 BQ 1 1 A
(9)
The equation above shows a 4×1 3D coordinate
points in the homogeneous form, which can be denot-
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ed as
is:
A
Q or BQ , and then the corresponding matrix
(z b p z e m z cnz l3 )2 L2
Q T Q
A
A
B
B
(10)
Branched Chain 6:
A
B
The homogeneous matrix T is then transformed
into a 4×4 matrix, as shown below:
AR
T B
0
A
B
(x bpx emx cnx b)2 (y b p y e m y cn e) 2 (18)
QB 0 1 A
(11)
(x dmx cnx )2 (y d d m y cny )2
(19)
(z d m z cnz l1 ) 2 L2
Considering the initial posture, the motion output
function of motion platform is turned to:
R E x 0 y 0 z h c li q0
3.2 Inverse Kinematics Model
RPY angle coordinate is 3D-transformed to represent
the motion platform, and the corresponding position
parameter is q x y z . Where, Euler
transformation angle of motion platform is , , ,
and the coordinate in the coordinate system {W} is
x, y, z . To simplify the calculation process, the coordinate is transformed as:
R Rx Ry Rz
l1 z dmz cnz [L2 (x d m x cn x ) 2 (20)
(y dmy cn y )2 (y dm y cn y d) 2 ]1 2
l2 z bpz emz cnz [L2 (bp x em x cn x (21)
x b)2 (bp y em y cn y y e) 2 ]1 2
(12)
From the equation above, the ball joint in the coordinate system {W} can be represented as:
Ci RCi (x, y, z)T
From the equations above, the expressions of motion inverse solutions for fitness simulation horse are:
(13)
Where, Bi , Ci are known, and then the constraint
can be accordingly obtained from the geometrical
relationship:
l3 z bpz emz cnz [L2 (x b bp x (22)
em x cn x )2 (y bp y em y cn y e) 2 ]1 2
l4 x H1 fpx [L2 ( y fp y ) 2
(z fpz h c) 2 ]1 2
l5 y ap y gmy H 2 [L2 (x a p x
BiC L
From the two-point distance formula, the functional
equations of time t for x, y, z , , , and l
can be obtained, corresponding to each branched chain
as follows:
Branched Chain 1:
(x ap x gm x a)2 (y ap y gm y H 2 l6 ) 2 (14)
(z ap z gm z h c) 2 L2
Branched Chain 2:
(x ap x gm x a)2 (y ap y gm y H 2 l5 ) 2 (15)
(z ap z gm z h c) L
2
2
Branched Chain 3:
(x fmx H1 l4 ) (y f p y )
2
( z fpz h c) 2 L2
2
(16)
Branched Chain 4:
(x bpx emx cnx b)2 (y b p y e m y cn e)2 (17)
(z b p z e m z cnz l3 )2 L2
Branched Chain 5:
(23)
(24)
g m x a)2 (z a p z g m z h c) 2 ]1 2
l6 y ap y gmy H 2 [L2 (x a p z g m z (25)
z h c)2 (a p x g m x x a) 2 ]1 2
This equation expresses the kinematical inverse solution of fitness simulation horse, through which it can
be seen that the expression structure is unique and
simple. Therefore, the design of orthogonal parallel
mechanical to control the fitness simulation horse is
reasonable and effective.
3.3 Study on the Control of Motion Platform
Branched Chains
In order to easily install the fitness simulation horse,
the semi-closed loop control was used in this paper to
control the spatial position and assure sufficient precision, rather than the fully-closed loop control directly
connecting the machinery to sensors.
As the running fitness simulation horse is on varied
load, and its speed also varies and is not stable, the
key is to control the current to make it run steadily.
Considering the application of the current closed loop
developed by Panasonic in the servo drive, a solution
with control principle shown below was proposed in
this paper:
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Position is
Simulation
Position regulator
known
Amplifier
Feedback or
Speed regulator
Current regulator
speed
output
Figure 3. Motion Platform Branched Control Chart
Figure 4. Comparison between Traditional Controller and Digital Simulation Controller
In this paper, in order to effectively control the position of fitness simulation horse, a three-layered
closed loop circuit was used, arranged from outside to
inside with position loop, speed loop and current loop,
so as to lessen the current changes in the phase position and amplitude and also to effectively control the
steadiness of the fitness simulation horse during the
entire movement.
k
u (k) k p e(t) k i T e(j) Td
j 1
kd
e(k)
T
In order to avoid any deviation, the digital simulation controller model was actually used, as shown in
the equation below:
u (k 1) k p (e(k 1))
k
k i T e(j) kd (e(k 1) e(k 2)))
j 1
4 CONTROLLER MODEL OF FITNESS SIMULATION HORSE
u (k) k p [e(k) T
Ti
e(j) T
d
j 1
e(k) e(k 1) (26)
]
T
ki kp
Ti
the
above
, k d k p Td
equation,
(29)
u(k) u(k) u(k 1)
e(k) e(k) e(k 1)
e(k 1) e(k 1) e(k 2)
Thus, it can be drawn that from the subtraction between two equations above:
u (k) k p [e(k) e(k 1)] k i Te(k)
Where, the differential time and integral time of the
controller are Td and Ti , the corresponding proportionality factor is k p , the deviation signal is e(t) , the
output is u (k) , and T is the sample cycle.
In
the
equation
above,
suppose
e(k) e(k) e(k 1) and simplify the calculation
process, and then it can be drawn that:
T
T k
u (k) k p [e(k) e(j) d e(k)] (27)
Ti j 1
T
From
kd
e(k)
T
Then, suppose:
A PID controller based on the control theory was used
to fully control the movement of fitness simulation
horse, with the model shown as follows:
k
(28)
if
, it can be drawn that:
kd
[e(k) 2e(k 1) e(k 2)]
T
(30)
As the fitness horse controller was improved, the
error effect was avoided, so that the model precision
was assured, the calculation became more efficient,
and the storage space also decreased.
5 EXPERIMENT OF FITNESS SIMULATION
HORSE BASED ON CONTROL THEORY
In order to validate the effectiveness of the controller
for fitness simulation horse, a simulation experiment
was conducted on this controller during its application
in the fitness simulation horse. The comparison be-
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tween the traditional controller and digital simulation
controller is shown in figure 4.
In addition, in order to observe whether the components in the model are proper linked, a dynamic
simulation experiment was conducted on the fitness
simulation horse, and the kinematic trajectories between the front and hind legs of fitness simulation
horse and the contact points on the platform plane
were drawn. As a man runs a circle, the fitness simulation horse also accordingly moves forward a cycle.
The kinematic trajectory for the front legs of fitness
simulation horse is shown in Figure 5 given below:
structure based on new control theory, this paper designed the fitness simulation horse based on new control theory and effectively controlled the motion platform. The main work is listed below:
1) Propose the control theory and set up an orthogonal parallel platform for the fitness simulation horse
by analyzing the advantages of fitness simulation
horse to human health; effectively control the fitness
simulation horse with the peripheral control system, so
as to shorten the response time and improve the efficiency of the entire system.
2) Establish the kinematics model according to the
platform characteristics. The final result was unique,
which therefore assured the stability and improved the
precision of the fitness simulation horse.
To sum up, this paper designed the fitness simulation horse based on the control theory and thus effectively controlled the system, which partly made progress in the control theory on fitness simulation horse.
However, this control theory still remains to be studied and further completed before being applied into
practice.
Figure 5. Displacement Curve of Front legs and Ground
Contact Point
REFERENCES
The kinematic trajectory for the hind legs of fitness
simulation horse is shown in Figure 6 given below:
Figure 6. Displacement Curve of Hind Legs and Ground
Contact Point
As seen from the simulation results above, the digital simulation controller is more stable and quickly
responsive within less time than the traditional controller. During the movement trajectory test, the
backward trajectory was quite level and smooth, and
the postures of front and hind legs greatly varied. One
of the break points occurring was because the tie rod
was under great pressure when it rose to the highest
point, and then a knee point appeared on the trajectory.
The simulation results showed that, the fitness simulation horse can effectively run under the control from
the controller based on the control theory.
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6 CONCLUSION
In the environment of applying the parallel pipe robot
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